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Proof step 3 from proof getbyte-drop-upper (previous step)

VFS_PAGE_SIZE * m + VFS_PAGE_SIZE ≤ n ⊦ (n / VFS_PAGE_SIZE ∈ content[m, buf] ⊃ content[m, buf][n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE] = (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]

User applied rule case distinction

And obtained the following new goals

Proof step 4:
n / VFS_PAGE_SIZE ∈ content[m, buf], VFS_PAGE_SIZE * m + VFS_PAGE_SIZE ≤ n ⊦ content[m, buf][n / VFS_PAGE_SIZE][n % VFS_PAGE_SIZE] = (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]

Rule argument

pos: right 1

Additional information

Used simplifier rules: zeropage-mod-pagesize: ⊦ (zeropage)[n % VFS_PAGE_SIZE] = zero;% ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content; (ws)